Cube Graph

There are 2n 2^n 2n vertices, labelled v0,v1,…,v2n−1 v_0, v_1, \ldots, v_{2^n-1} v0​,v1​,…,v2n−1​. Draw an edge between va v_a va​ and vb v_bvb​ if and only if the binary representations of a a a and b bb differ in exactly one digit.

We would like to find a path along the cube graph Cn C_n Cn​ that crosses each edge exactly once, and begins and ends at the same vertex. For C2 C_2 C2​ this is possible: start at 0, move to 2, move to 3, move to 1, move back to 0.